Recalling a Witness: Foundations and Applications of Monotonic State

Abstract

We provide a way to ease the verification of programs
whose state evolves monotonically.
The main idea is that
a property witnessed in a prior state can be soundly recalled
in the current state, provided (1) state evolves according to a
given preorder, and (2) the property is preserved by this preorder.
In many scenarios, such monotonic reasoning yields concise
modular proofs, saving the need for explicit program invariants.
We distill our approach into the monotonic-state monad, a
general yet compact interface for Hoare-style reasoning
about monotonic state in a dependently typed language.
We prove the soundness of the monotonic-state monad and use it as a
unified foundation for reasoning about monotonic state in the
F* verification system.
Based on this foundation, we build libraries for various mutable data
structures like monotonic references and apply these libraries at
scale to the verification of several distributed applications.